...at a point : the theorem is called the parallelogram of forces, and may be thus enunciated. If two forces acting at a point be represented in magnitude and direction by two straight lines drawn from that point, and if a parallelogram be constructed having these two lines...

...magnitude by AD, the diagonal of the parallelogram, of which AB and AC are the sides. Jf three forces represented in magnitude and direction by the sides of a triangle taken in order act at a point, ihey mil keep it in equilibrium. Let three forces, AB, BC, CA represented in magnitude...

...: Q : R : : sin QR : sin R"? : sin PQ. 23. POLYGON OF FORCES. If any number of forces acting upon, a point be represented in magnitude and direction by the sides of a polygon taken in order, they will be in equilibrium. Let forces represented by the sides of the polygon...

...two.) And conversely, (2) If three forces acting at a point ~be represented in direction and magnitude by the sides of a triangle taken in order, they will be in equilibrium. (1) Let the forces P, Q, R acting at the point 0 be in equilibrium, and be represented by OE, OG, OH;...

...acting at a point. The theorem is called the Parallelogram of Forces, and may be thus enunciated. If two forces acting at a point be represented in magnitude and direction by two straight lines drawn from that point, and if a parallelogram be constructed having these two lines...

...which lies between them by a quantity as small as we please ; hence we conclude, generally, that if two forces acting at a point be represented in magnitude and direction by two adjacent sides of a parallelogram, their resultant will have the direction of the diagonal of the...

...bank. Shew that, if the boat be loosed from its moorings, it will swing round to the opposite bank. 14. If three forces, acting at a point, be represented in magnitude and direction by three straight lines drawn from that point, then, if the forces are in equilibrium, the triangles formed...

...their difference, this is the algebraical sum of the forces. 32. Parallelogram of Forces.—If any two forces acting at a point be represented in magnitude and direction by the two sides of a parallelogram, the diagonal of the parallelogram passing through the given point will...

...may be represented by the sides of the triangle BDF, viz., BD, DF, F B. 47. The converse of this — If three forces, acting at a point, be represented...direction by the sides of a triangle, taken in order, they are in equilibrium, — is also true, and may be easily proved from the same figure. 48. Polygon Of...

...supposition. 83d If three forces acting upon a point can be represented in magnitude and direction by three sides of a triangle taken in order, they will be in equilibrium. At the point JP, Fig. 22, let three forces, F, Fr, J2,be applied in the directions PA, PB, PC, these...